3-D Drawing and Geometry

by Cathi Sanders

A Math Forum Summer Institute Project

Perspective Drawing

It is relatively easy to sketch in oblique and in isometric, but
there is a third type of drawing that more closely resembles the
way we see things in the real world: perspective drawing.

When we look at the world around us, we see objects in perspective,
as in this photograph of the Armory Mewata in Calgary, Canada, from
McGill University's course,
Canadian Architecture 101:

Notice that the lines on this type of drawing are different from those
in either isometric or oblique drawings. In this type of perpsective
drawing, which is called two-point perspective, there are three types of
lines: lines that converge to the left at a point (called the
Vanishing Point Left), lines that converge to the right at a point
(called the Vanishing Point Right), and vertical lines. The drawing
below illustrates these types of lines on the Calgary Armory
Building:

When drawing in perspective, you can vary your point of view. This
is not true in either isometric or oblique drawings, both of which have
a fixed point of view and appearance. Changing the location of the
vanishing point will cause a change in the appearance of the
perspective drawing.

You can use this JavaSketchpad applet to play
with perspective. Drag any of the red points in the drawing.